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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
Choose the correct answer from the given four options:
If $\triangle\text{ABC}\sim\triangle\text{QRP},\frac{\text{ar}(\text{ABC})}{\text{ar}(\text{PQR})}=\frac{9}{4},$ AB = 18cm and BC = 15cm, then PR is equal to:
  • ✓
    10cm
  • B
    12cm
  • C
    $\frac{20}{3}\text{cm}$
  • D
    8cm
✓

Answer

Correct option: A.
10cm
Given, $\triangle\text{ABC}\sim\triangle\text{QRP},$ AB = 18cm and BC = 15cm

We know that, the ratio of are of two similar triangles is equal to the ratio of square of their corresponding sides.
$\therefore\frac{\text{ar}(\triangle\text{ABC})}{\text{ar}(\triangle\text{PQR})}=\frac{(\text{BC})^2}{(\text{RP})^2}$
$\text{But given, }\frac{\text{ar}(\triangle\text{ABC})}{\text{ar}(\triangle\text{PQR})}=\frac{9}{4}$
$\Rightarrow\frac{(15)^2}{(\text{RP})^2}=\frac{9}{4}$
$\Rightarrow\big(\text{RP})^2=\frac{225\times4}{9}=100$
$\therefore\text{RP}=10\text{cm}$

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